Strain superlattices and macroscale suspension of graphene induced by corrugated substrates

We investigate the organized formation of strain, ripples, and suspended features in macroscopic graphene sheets transferred onto corrugated substrates made of an ordered array of silica pillars with variable geometries. Depending on the pitch and sharpness of the corrugated array, graphene can conformally coat the surface, partially collapse, or lie fully suspended between pillars in a fakir-like fashion over tens of micrometers. With increasing pillar density, ripples in collapsed films display a transition from random oriented pleats emerging from pillars to organized domains of parallel ripples linking pillars, eventually leading to suspended tent-like features. Spatially resolved Raman spectroscopy, atomic force microscopy, and electronic microscopy reveal uniaxial strain domains in the transferred graphene, which are induced and controlled by the geometry. We propose a simple theoretical model to explain the structural transition between fully suspended and collapsed graphene. For the arrays of high density pillars, graphene membranes stay suspended over macroscopic distances with minimal interaction with the pillars' apexes. It offers a platform to tailor stress in graphene layers and opens perspectives for electron transport and nanomechanical applications.